Abstract

Silica microspheres are probed with a dual comb interferometry setup. The impulse responses of these microresonators are measured with a temporal resolution smaller than 400 fs over more than 200 ps. The amplitudes and phases of the impulse responses are interpreted as providing sensing information. The more familiar transmission spectra corresponding to the measured impulse responses are also calculated and shown. Sensing is demonstrated by varying the concentration of isopropanol in de-ionized water surrounding the microsphere and by binding bovine serum albumin on the silanized microsphere surface.

1. Introduction

Optical sensing with whispering gallery mode (WGM) microresonators is routinely achieved in the frequency domain where the precise spectral shift of a single high finesse mode quantifies changes in the surrounding environment [1

]. The study of the interaction between light propagating in WGMs and analytes on the optical microcavity surface could help lowering even further the detection limit. In fact, valuable information can be obtained with ultrafast optical methods in the time-domain as well as multimodal analysis in the frequency domain. Indeed, more information can be gathered by monitoring the shifts of multiple modes [5

], as the probed material is unlikely to have a perfectly flat frequency response in polarizability. Also, without this additional information, a reference spectrum or another parameter must be known a priori to calibrate the detection [6

]. The lower quality factor of these microspheres sacrifices the mode finesse, but the resulting loss in sensitivity is somewhat compensated with an evanescent field penetrating deeper into the probed material as the radius decreases [13

Beyond manipulating the modal spectrum, MWGMs could also be handled with an apt choice of probing method. Time-domain studies have already revealed interesting characteristics of femtosecond pulse propagation in WGMs [14

]. An interesting interferometric probe to consider is the dual frequency comb (FC) since it provides the impulse response of resonator in the time domain, both in phase and amplitude. The complex transmission spectrum is also easily retrieved via a numerical Fourier transformation. FCs are especially well suited to characterize MWGMs as they are based on ultrafast laser pulses covering a broad spectrum at gigahertz to megahertz resolution with millisecond to microsecond acquisition times [17

]. FCs are already a great spectroscopic tool in macroscopic transmission experiments, but somewhat lack detection sensitivity. More specifically, spectroscopy measurements using frequency combs have demonstrated that with a spectral sampling by the comb teeth of 100 MHz, a spectral signal-to-noise ratio of 440 can be attained in a 2 seconds measurement time [22

], but achieved simultaneously on the tens or hundreds of WGMs present on the 10 THz spectral bandwidth of the combs. Regardless of the chosen spectroscopic approach, detection sensitivity can be improved by extending the detection path length to keep the light probing the material of interest for longer times, either in a cavity [24

] or a microcavity as proposed here. The strengths of these microresonators and the FCs are thus quite complementary. Generating FCs with nonlinear processes in microcavities is already a steadily progressing field [25

]. In this article, it is shown that dual FC spectroscopy can be used to improve MWGM sensing. Interpretation of the microresonator impulse response in amplitude and phase provides direct information on path lengths of a single pulse in the sphere, in a manner related to cavity ring down spectroscopy [15

]. The information on the impulse response is linked via the Fourier transformation to the spectral variations normally used in MWGM sensing. The relative phase shift of the pulses exiting the microresonator after each round-trip is notably linked to the modes’ spectral shift. This is demonstrated by varying the concentration of isopropanol in de-ionized water surrounding the microsphere and by binding bovine serum albumin on the silanized microsphere surface.

2. Experiment

Silica microspheres are fabricated by melting the end of a single mode optical fiber in the arc of a commercial PM-fiber fusion splicer. The arc discharge parameters are taken from [28

]. During the discharge, surface tension pulls the molten silica into a spherical shape. The deformation caused by gravity during the sphere formation is partially corrected by conti-nuously rotating the fiber using the motorized fiber holder. Microspheres with a diameter of ~360 μm are obtained with standard SMF-28 optical fiber. Smaller microspheres with diameters ranging from ~60 μm to ~275 μm are obtained from the tip of tapered fibers. The light is coupled into the microcavity through the evanescent field of a tapered fiber typically 2-3 μm in diameter. The taper is fabricated by stretching a stripped fiber between two translational stages while the fiber is softened in a hydrogen flame. Once the tapering is completed, drops of transparent epoxy are used to secure the tapered fiber into a semi-cylindrical quartz holder. This quartz holder is finally fixed into a hermetic sample cell that allows the injection of liquids. Since the microspheres do not have ultra-high quality factors, it is not necessary to control the temperature inside the sample cell. A microsphere is held on a X-Y-Z stage above the sample cell and is brought into contact with the thinner region of the taper and stays into place due to silica-silica van der Waals interactions. Initial alignment is made using a CCD camera and a visible light source connected to the biconical taper. Finer alignment of the microsphere and preliminary transmission measures are made with a 1510-1600 nm EXFO IQ-2600B tunable laser source and a power meter. Once resonances are recorded, the tapered fiber is connected to the frequency comb laser.

The comb probing the microresonator repetitively generates its impulse response, which is sampled using a second comb at a slightly different repetition rate [29

]. The detuned repetition rates generate pulse pairs with a gradually increasing inter-pulse delay. Because the cavity is placed in an interferomeric setup between the two combs, the phase information is preserved [20

]. The measured interferogram (IGM) holds information on the impulse response of the sample, convolved with the cross-correlation of the laser fields. Fourier-transforming the IGM yields the complex spectrum [20

] of the optical field after the microresonator. To achieve this correctly, the delay between the pulses must increase linearly, which corresponds to an equidistant sampling grid. Since the variation of the repetition rates and carrier-envelope offsets (CEO) over time produces a variation of the sampling grid, a referencing technique using two continuous wave (CW) lasers is used to track the timing and the phase between the two pulses of each pair [21

]. Once these variations are removed, successive IGMs can be averaged to increase the signal-to-noise ratio (SNR). This method provides high spectral resolution, an important parameter when sampling microresonators with long impulse responses.

Fig. 1 Experimental setup used to probe microspheres. Two polarization controllers (PC) are used to choose the polarization before and after the microsphere. The acquisition chain includes a balanced detector (D), an electrical amplifier (RF Amp.), a low-pass filter (LPF) and an analog-to-digital converter (ADC).

describes the experimental setup used to sample microspheres. The setup is made of two “c-fiber” Menlo System mode-locked erbium fiber lasers. The repetition rate of both lasers is around 100 MHz. This gives a spectral resolution of 1.25 pm at 1550 nm whichcorresponds to the measurement of a 10 ns impulse response. The repetition rate difference between the two lasers is set to 100 Hz, which gives 100 IGMs per second. The pulses bandwidth is 80 nm around 1550 nm. The first comb passes through the fiber taper and is partly coupled in the microresonator. The field emanating from the other side of the taper is then mixed with the second frequency comb using a fiber coupler. The polarization controller (PC) before the taper is used to select the polarization of the evanescent light that will enter the microsphere. The second controller is used to match the polarization between both arms before mixing. The optical signal is converted to an electrical signal using a balanced Thorlabs PDB130C (350 GHz bandwidth) detector (D). A Mini-Circuits BLP-50 + 48 MHz low-pass filter is used to prevent aliasing given the 100 MHz comb repetition rate. The amplifier before the analog-to-digital converter (ADC) serves to use all the dynamic range available at the ADC to reduce thermal and quantization noises. The 14 bits ADC operates at 122 MHz. The data is transferred to a computer for post-processing correction and analysis.

Propagation through optical fiber induces dispersion to the pulses. The difference between the path length of the first comb and the second comb will chirp the IGM. This chirp causes no effect when analyzing the amplitude in the spectral domain but is undesirable in the time domain. In the time domain, the chirp broadens features. This can limit the ability to distinguish nearby events. This is especially true when probing a rich impulse response where regularly spaced peaks are expected. It is however possible to remove this chirp by post-processing. The first pulse measured in the impulse response corresponds to light that went straight through the taper, having minimal interaction with the microresonator. This pulse is used to retrieve the instrumental dispersion contribution. This is done by computing a short Fourier-transform around the center of the IGM and by estimating the phase in this spectrum. A third order polynomial is fitted on the phase previously calculated. Doing an inverse Fourier transform on the reversed phase signal will generate a filter having the opposite chirp. By applying this filter to the IGM, the dispersion coming from the instrument is eliminated. This also yields a higher SNR in the time domain because pulses are compressed and have higher amplitude while the amount of noise is unchanged. Pulses will be more defined, making the time domain analysis easier.

3. Microsphere transmission spectrum

A small microsphere of ~88 µm with a simple modal structure was originally chosen to investigate the frequency spectrum of a microresonator with a dual FC. In a more geometrical picture, frequencies such that an integer number of wavelengths fit the round-trip path in the microresonator correspond to the polar modes, with the mode number l set by the number of nodes. As the microsphere size decreases, the frequencies fulfilling this condition spread out. When the microsphere is immersed in a phosphate buffered saline (PBS), the wide free spectral range (FSR) of 6 nm yields only 5 polar modes for each polarization, transverse electric (TE) and transverse magnetic (TM), as shown on the 30 nm spectral range in Fig. 2(a)

The choice of refractive index contrast, here between silica at 1.46 and PBS at ~1.34, also impacts the FSR since the wavelength is decreased in a medium with higher refractive index, hence it also affects the conditions to fit an integer number of wavelengths in the microsphere. In Fig. 2(a), only the positions of the transmission minima calculated with the Mie solution are indicated for a perfect sphere [8

], the regular structure is preserved but numerous m-modes have appeared within the FSR, as seen in the two experimental spectra of Fig. 2(b) and 2(c).

The spectrum in Fig. 2(b) was measured with a tuneable laser while Fig. 2(c) was obtained using the dual FC setup. The line shape of the transmission dips looks similar in both cases with an identical width indicating this measure is not limited by spectral resolution, but instead by the microresonator itself. The discrepancy in the structure of the observed modes suggests mode selectivity: not all azimuthal modes are excited uniformly depending on the coupling between fiber and microresonator. The stability of the system against thermal drift, vibrations or other mechanical perturbations was often monitored during five minutes and the spectra were sufficiently reproducible to conclude that the fiber / microresonator alignment is unlikely to be perturbed when the excitation source is changed at the extremity of the fiber. The most likely cause of coupling variations is the different polarizations of the sources. Figure 3

Fig. 3 Sensitivity to excitation polarization: the same modes are present in both curves corresponding to distinct polarizations, but their relative intensities vary (Media 1).

explores the impact of modifying the polarization on the WGM modal structure. Theaccompanying movie shows progressively how certain modes become enhanced to later almost disappear as the input polarization of the tunable laser source is varied. Input polarization thus emerges as a probing parameter useful to simplify the MWGM structure by selecting preferentially either the TE or the TM modes.

4. Sensing with the impulse response

Sending and probing light pulses in a microcavity with dual FCs can provide not only the high resolution spectrum necessary for sensing, but also ultrafast dynamical information about the interaction of light with the material surrounding the microresonator. We first looked into refractive index sensing of a homogeneous solution by mixing isopropyl alcohol (n2 = 1.377) with de-ionized water (n2 = 1.332) at concentrations of 0%, 10%, and 19% v/v (Fig. 4

Fig. 4 (a) Impulse response of a ~73 µm microsphere in solutions of isopropanol in water at different concentrations. (b) Zoom on the initial pulse going through the fibre taper only. (c) Zoom on the pulse having entered the microresonator and leaving after a single revolution. The bright traces are the real part of the IGMs, while the faint ones are the magnitude.

). Care was taken to minimize thermal fluctuations by placing both liquids at room temperature for an extended period of time before mixing and by ensuring thermalization of the ~73-µm microsphere in water. The data was averaged over 300 IGMs when ~45 s elapsed after the isopropanol injection, hence leaving sufficient diffusion time in the sample cell to obtain a homogeneous blend [3

The impulse responses of the microsphere in the isopropanol solutions are shown in Fig. 4(a). The optical time delay grid is obtained by monitoring the time delay between the combs’ pulse pairs. Since the instrumental dispersion is compensated, these impulse responses can be interpreted as a pulse with a maximal duration of 400 fs entering the microresonator. Its front tail travels roughly 82 μm in the SiO2 microresonator and does not overlap its own back tail by the time the input coupling is completed. The compensated pulse becomes significantly shorter than the cavity length, occupying at most 36% of the circumference, thus theconditions for ballistic trajectories of optical wave packets are satisfied [31

]. Figure 4(c) zooms on the first completed round-trip after ~1.13 ps corresponding to a group velocity of 2.03e8 m/s. As can be expected from greater absorption of isopropanol, the intensity envelope of the pulse train decays rapidly, indicating significant losses in the microresonator corresponding to short cavity lifetimes. The FSR ≈7.3 nm seen on Fig. 5

Fig. 5 Transmission spectra obtained from the Fourier transform of the impulse response of a ~73 μm microsphere immersed in (a) 0%, (b) 10%, and (c) 19% v/v isopropanol in water solution.

matches what is calculated from the round-trip time and corresponds to polar l-mode spacing. The transmission spectrum in Fig. 5 also shows azimuthal m-modes regularly spaced by ∆λ ≈0.58 nm. An equivalent structure is found in the impulse response at a delay ∆T = λ2/c∆λ ≈14 ps where output pulses are slowly rising and decaying again.

When the isopropanol concentration increases, the diminishing refractive index contrast and increasing absorption caused the usual broadening of the resonances in Fig. 5 due to weaker confinement of the light with an evanescent field penetrating deeper in the solution. This readily translates to decreasing cavity lifetimes in the IGMs of Fig. 4 with the amplitude of the rightmost pulses disappearing progressively. A more surprising feature seen in the magnitude plot as a function of time is that pulses appear to couple out of the microsphere at the same time, independently of the refractive index n2. In other words, changes in group velocity are too small to be observed, but we can turn to the phase of the light pulses instead. Indeed, the phase velocity of a wave slows down with increasing refractive index resulting in a greater phase change per unit length according to the well-known relation on the wavenumber k = nk0. FCs are well suited to confirm this statement since they allow direct observation of phase changes by plotting the IGM’s real part instead of its magnitude. Comparing these plots for the three isopropanol solutions with distinct refractive indices, the expected phase appearsright after the first microsphere round-trip in Fig. 4(c) relative to the IGMs of Fig. 4(b) kept aligned and in phase when the pulse is only passing through the taper. In the former figure, the decreasing phase velocity is clearly manifested by the delayed wavefronts taking more time to go around the microsphere immersed in the isopropanol-water mixture.

This additional information gathered with the interferometric FC setup can also be very useful for bio sensing to get further insights into more complex systems. Moreover, the acquisition time for a full IGM is much less than a second, which allows monitoring of kinetic processes on the timescale of minutes or possibly less. Hence, we have chosen to probe the diffusion-limited process of bovine serum albumin (BSA) adsorption on the surface of a ~77 μm silica microsphere. The surface of the latter was plasma cleaned and silanized with aminopropyltriethoxysilane [33

]. The sample cell was first filled with thermally equilibrated phosphate buffer saline, then BSA was injected while the frequency comb laser was active and the solution was gently stirred. The final BSA concentration was 1.5 mM, which is ~8 times the concentration necessary for monolayer adsorption [34

]. The IGM observation time was 117 ms yielding a signal-to-noise ratio of 316 and measurable WGM shifts of ~340 fm on the full 1530-1600 nm wavelength range with our FC setup having a frequency resolution of 14 GHz. Much smaller shifts could be detected using longer acquisition times, hence becoming comparable to the performances reported by K. Vahala et al. [4

Fig. 6 (a) Impulse response of a silanized microsphere with increasing BSA surface coverage at different times after the injection. (b) Zoom on the pulse after a single round-trip showing a progressive phase-shift from red to blue while keeping the same envelope in magnitude. (c) Zoom on the pulses after 16 and 17 round-trips. The bright traces are the real part of the IGMs, while the faint ones are the magnitude.

with increasing BSA concentration is similar to those recorded after isopropanol injections, but here we can follow the IGM evolution much more gradually especially in the videos (Fig. 7

) made from the data in both the time and frequencydomains. Though the BSA affects light propagation in the microcavity only very locally through a part of the evanescent field, the phase of the light pulse is still measurably modified during the first round-trip. The progressive de-phasing from red to blue in Fig. 6(b) reaches ~2.1 rad after 510 s of diffusion time. Since this first lap is completed in ~1.14 ps which is much shorter than typical thermal relaxation times on the order of microseconds, it seems thermo-optic effects cannot contribute significantly to the de-phasing observed. Thus, the electromagnetic wave and the BSA would mainly interact through the real part of the polarizability, Re{α}, via the reactive mechanism [35

]. A careful analysis of this de-phasing and its relation to the phase velocity of the light pulse as a function of BSA concentration could thus give indications on the reactive component of single molecule polarizability.

5. Conclusions

Dual FCs emerge as a powerful probe of optical microcavity dynamics through its impulse response both in amplitude and phase. The familiar transmission spectrum is obtained by a Fourier transform of the impulse response and the quasi-periodic features both in the frequency and time domains can be related together: from the modes in the former to the pulse trains in the latter. The usefulness of this probe was demonstrated for both refractive index sensing and biosensing. A microsphere immersed in solution of isopropanol and de-ionized water exhibited both the usual spectral shift and a phase shift in the pulses exiting the microresonator after probing its surroundings. A gradual phase shift was also measured upon BSA coverage, independent of any heating effect, showing the high potential sensitivity of the technique.

Acknowledgments

The authors acknowledge financial support from Le Fonds de recherche du Québec – Nature et technologies (FQRNT), Karel Boissinot and Maurice Boissinot for providing BSA as well as precious technical support from Patrick Larochelle and Vincent Tremblay. The authors also wish to thank Jean-Daniel Deschênes and Sylvain Boudreau for stimulating discussions.

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